We had the same after the Olympics, when someone was complaining about how many of the athletes came from public school backgrounds.
The reason in both cases is quite simple. As a general rule (yes there will be exceptions) it is only in the public schools that drama clubs still flourish, there are still school theatres that are actively used, active music clubs, recording studios, etc. It also only tends to be public schools where non mainstream sports are still actively pursued.
If the MP in question wants more people from less privileged backgrounds in the arts and athletics then he needs to improve the opportunity for children in state schools to experience these activities, i.e. more facilities, and more teachers willing to participate in out of hours activities.